Closing this because none of this is Delta specific. FT is well populated with dozens of existing threads that answer your questions. None of this is a dig at our Newlywed and their spouse… just some housekeeping.

Taking off my mod hat for a minute… first, relax. The airlines and TSA have dealt with this thousands of times. It’s just bureaucracy.

lindros2 is on the mark for the order and is 100% correct.

In addition : you can book tickets any time using whichever name is available for where you are in the process. It takes months to do it all. Just carry the marriage certificate and things will be fine. It may briefly cause TSA precheck issues if the ticket is bought under a mismatched name, but I don’t see a ton of complaint threads vs the frequency I’d expect, so there must be some sort of tracking.